Final answer:
Using the Pythagorean theorem, since Booneville is 3 kilometers from the airport and the distance between Booneville and Hillsboro is 5 kilometers, we find that Hillsboro is 4 kilometers due east of the airport.
Step-by-step explanation:
The question requires the use of the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this scenario, we have Booneville which is 3 kilometers due north of the airport, and Hillsboro which is due east of the airport. The distance between Booneville and Hillsboro is 5 kilometers. If we imagine this as a right-angled triangle, with Booneville and Hillsboro as points on the hypotenuse, and the airport as the right angle vertex, we can use the Pythagorean theorem to solve for the distance of Hillsboro from the airport.
Let's denote the distance from the airport to Hillsboro as 'x'. According to the Pythagorean theorem:
3^2 + x^2 = 5^2
9 + x^2 = 25
x^2 = 25 - 9
x^2 = 16
x = sqrt(16)
x = 4
Therefore, Hillsboro is 4 kilometers due east of the airport.